Find the area between the graphs of and on the interval .
First, we draw the graph, shading the region between the two graphs in blue.
For this exercise, since and cross in the interval we are interested in (and we are calculating the area between the graphs, so we’re really looking at the integral of ) we split the integral into two pieces (at the point the functions cross). We have on and on ; thus, we have
Took me two days staring at my answer of 1/3*(8-4*sqrt2) to realise I made a simple sign error subtracting the final 2/3 instead of adding it. If anyone wants to know how my 2023 began.